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Fix in Consider the real linear map

given by

(a) With respect to the basis B = {1, i, j, k}, find the associated matrix for .
(b) Find the associated matrix A (sub alpha bar) for M (sub alpha bar). Compare with (a).
(c) Compute det(A sub alpha) and det (A sub alpha bar). Interpret.

See attached file for full problem description.


Solution Preview

In order to be able to write them, I will use a and b instead of alpha and beta; I will also use M_a as a notation for M sub a, and conj(a) will mean a bar (the conjugate of a). The problem does not specify, but I assume H means the algebra of quaternions.
(a)our element a in H can be uniquely written as x+y*i+z*j+t*k, where x,y,z,t are ...

Solution Summary

This shows how to find associated matrices for a given linear map.